The median offers several advantages as a measure of central tendency. While pinpointing exactly four merits can be subjective and depend on the context, here are four key benefits, drawing from the provided reference and expanding on them:
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Rigidly Defined and Easy to Understand: Like the mean, the median has a clearly defined method for calculation. This makes it easy to understand and calculate, especially in simple datasets. There's no ambiguity about how to find the median.
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Not Affected by Extreme Values (Robustness): This is arguably the median's greatest strength. Unlike the mean, the median is not greatly influenced by outliers or extreme values. This makes it a more reliable measure of central tendency when dealing with skewed distributions or data containing errors. As the reference example shows, even adding extremely large values to a dataset doesn't dramatically shift the median.
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Can be Determined Graphically: The median can be visually identified on a cumulative frequency curve (ogive) by finding the value corresponding to the 50th percentile. This graphical determination offers a quick and easy way to estimate the central tendency without complex calculations.
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Applicable to Open-Ended Distributions: Unlike the mean, the median can be determined even when the data has open-ended classes (e.g., "more than 100"). Since the median focuses on the middle value rather than the specific values themselves, the presence of open-ended classes doesn't hinder its calculation. The mean, on the other hand, would require making assumptions about the values within the open-ended class.
In summary, the median's robustness to outliers, clear definition, graphical determinability, and applicability to open-ended distributions make it a valuable measure of central tendency in various statistical contexts.
